How to increase frequency of a repetive animated movement?
Found a possible solution myself.
Steps to perform:


Animate one motion manually. This motion will be repeated and speed
up in later steps.
For the NLA strip created that way set the count of repeats in the
N-key panel.
In the timeline set the start and end to the first frame and to the
last frame of the NLA-strip including all repetition.
Deselect all strips in the NLA editor.
Only Select the NLA strip in question.
Now bake the animation. I choose "object" to be baked. This can take
quite some time.
The result is an additional strip, which includes the complete
animation as it had been animated by hand frame by frame.
Now it is possible to animate the flow of time of this newly created
strip easily.
Disable the the original strip (the one with the repetition modifier
set). You can use this as an backup for later modifications.
Play the animation.


This is one possible solution, which leads to what I wanted. I am sure, there will be other options to fine tune the result and especially speed up the baking time.